A method for spatially modulating illuminating light is known a method of observing a specimen such as a biological specimen or the like with super-resolution (see patent documents 1, 2, non-patent documents 1, 2 or the like). According to this method, the spatial frequency of the structure of the specimen is modulated by spatially modulated illuminating light, and information of the spatial frequency having high resolution exceeding the limit of resolution is contributed to the image formation of the optical system of the microscope.
However, in order to observe a super-resolved image, a modulated image of a specimen (modulated image) is required to be demodulated. The demodulation method is roughly classified into two kinds of methods, optical demodulation (see non-patent documents 1, 2) and calculation-based demodulation (see patent documents 1, 2). The optical demodulation is implemented by re-modulating the modulated image by using a spatial modulator such as a grating or the like.    Patent Document 1: Japanese Unexamined Patent Application Publication No. Hei 11-242189    Patent Document 2: Specification of U.S. Re-issued Pat. No. 38307    Non-patent Document 1: W. Lukosz, “Optical systems with resolving powers exceeding the classical limit. II”, Journal of the Optical Society of America, Vol. 37, PP. 932, 1967    Non-patent Document 2: W. Lukosz and M. Marchand, Opt. Acta. 10, 241, 1963